What Dr Dave said. The game sequence works happily there - I'd like to say it's good tactical manoeuvre on the American part, pinning or drawing the Hetzers fire with the infantry or arty whilst the tank works to the flank to pot it and break the German defence line, but I don't think the German did *anything* to stop it. Although it is an example game, and therefore not indicative of "real play", I guess.
The Hetzer has a 25cm Initiative range, and could likely (and should have) suppressed it on a free from enemy Op Fire first action previous turn, then either finish it with ordered actions or start popping shots to suppress the supporting infantry. Given German CVs and the decent dice on the Hetzer it could probably keep the whole bally lot stopped for a couple of turns on its own
I think the video shows less an issue with Initiative and more a very poor set of decision on the German COs part
Presumably due to it being a "training game", or possibly "IRL" him being a shell shocked 16y/o with two weeks training faced with an insurmountable opposition
Edit: I'd also recommend playing through a few games where similar situations are likely to come up and trying out all the options available to both sides; I suspect you'll find it's not the issue you think it is...